First Betti number of real Calabi-Yau hypersurfaces: examples

TL;DR

This paper explores the topology of real Calabi-Yau hypersurfaces in toric varieties, providing new methods to compute their first Betti number using mirror symmetry, with implications for their topological classification.

Contribution

It introduces a new theorem for calculating the first Betti number of real Calabi-Yau hypersurfaces via mirror symmetry, expanding understanding of their topology.

Findings

New theorem for Betti number computation

Applications to topology of real Calabi-Yau hypersurfaces

Insights into mirror symmetry implications

Abstract

Continuing the investigation of real Calabi-Yau hypersurfaces in toric varieties obtained by patchworking, we present a new theorem concerning the computation of their first Betti number using mirror symmetry. Although the proof of this result will appear elsewhere, we focus here on its consequences and applications to the topology of real Calabi-Yau hypersurfaces.